Image-based flow decomposition using empirical wavelet transform

We propose an image-based flow decomposition developed from the two-dimensional (2-D) tensor empirical wavelet transform (EWT) (Gilles, IEEE Trans. Signal Process., vol. 61, 2013, pp. 3999–4010). The idea is to decompose the instantaneous flow data, or their visualisation, adaptively according to the averaged Fourier supports for the identification of spatially localised structures. The resulting EWT modes stand for the decomposed flows, and each accounts for part of the spectrum, illustrating fluid physics with different scales superimposed in the original flow. With the proposed method, decomposition of an instantaneous three-dimensional (3-D) flow becomes feasible without resorting to its time series. Examples first focus on the interaction between a jet plume and 2-D wake, where only experimental visualisations are available. The proposed method is capable of separating the jet/wake flows and their instabilities. Then the decomposition is applied to an early-stage boundary layer transition, where direct numerical simulations provided a full dataset. The tested inputs are the 3-D flow data and their visualisation using streamwise velocity and $\lambda _{2}$ vortex identification criterion. With both types of inputs, EWT modes robustly extract the streamwise-elongated streaks, multiple secondary instabilities and helical vortex filaments. Results from 2-D stability analysis justify the EWT modes that represent the streak instabilities. In contrast to proper orthogonal decomposition or dynamic modal decomposition that extract spatial modes according to energy or frequency, EWT provides a new strategy for decomposing an instantaneous flow from its spatial scales.